Finite Group Databasebeta

← C3×#81710 #11896118

Subgroups — C3×#81710 #11896118

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 737 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5713C211yesmaximal, characteristic, complemented
2C3×#5690C211yesmaximal, characteristic, complemented
3C32×#490C211yesmaximal, characteristic, complemented
4C3×#5072C211yesmaximal, characteristic
5C3×#5063C211yesmaximal, characteristic, complemented
6C3×#4787C211yesmaximal, characteristic, complemented
7C3×#4787C211yesmaximal, characteristic, complemented
8C3×#4785C211yesmaximal, characteristic, complemented
9C3×#4768C211yesmaximal, characteristic, complemented
10C3×#4766C211yesmaximal, characteristic, complemented
11C3×#4765C211yesmaximal, characteristic, complemented
12C3×#4759C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4701C211yesmaximal, characteristic, complemented
16C3×#3370—31nomaximal
17#81710C311yesmaximal, characteristic, direct product factor
18C32×#127C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C3×#936—21no—
21C3×#936C2211yescharacteristic
22C3×#936C2211yescharacteristic
23C3×#935—21no—
24C3×#935—21no—
25C3×D4×Dic3—21no—
26C3×D4×Dic3C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C3×#897—21no—
32C3×#896—21no—
33C3×#896—21no—
34C3×#893C2211yescharacteristic
35C3×#893C2211yescharacteristic
36C3×D3×C4⋊C4—21no—
37C3×#890C2211yescharacteristic
38C3×#888C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#102C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#97C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#559—31no—
62C3×#554—31no—
63#5713C2×C311yescharacteristic, complemented
64#5690C2×C311yescharacteristic, complemented
65C3×#490—21no—
66C3×#490D311yescharacteristic, complemented
67C3×#490C2×C311yescharacteristic, complemented
68C3×#489—31no—
69C3×#488—31no—
70C3×#479—31no—
71C3×#478—31no—
72C3×#474—31no—
73C3×#463—31no—
74C3×#463—31no—
75C3×#459—31no—
76C3×#446—31no—
77C3×#442—31no—
78C3×#440—31no—
79C3×C4×D8—31no—
80#5072C2×C311yescharacteristic
81#5063C2×C311yescharacteristic, complemented
82#4787C2×C311yescharacteristic, complemented
83#4787C2×C311yescharacteristic, complemented
84#4785C2×C311yescharacteristic, complemented
85#4768C2×C311yescharacteristic, complemented
86#4766C2×C311yescharacteristic, complemented
87#4765C2×C311yescharacteristic, complemented
88#4759C2×C311yescharacteristic, complemented
89#4756C2×C311yescharacteristic, complemented
90#4710C2×C311yescharacteristic, complemented
91#4701C2×C311yescharacteristic, complemented
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6D411yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C42C2311yescharacteristic
112C3×#217—21no—
113C3×#217—21no—
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#213—22no—
119C3×#213—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×#204—22no—
138#3370—31noSylow
139C2×C3×SD16—31no—
140C2×C3×D8—31no—
141C2×C3×D8—31no—
142C3×C4⋊Q8—31no—
143C3×#127—21no—
144C3×#127C2×D311yescharacteristic
145C3×#127C22×C311yescharacteristic
146C3×#125—21no—
147C3×#125—31no—
148C3×#125C2×D311yescharacteristic
149C3×#125C22×C311yescharacteristic
150C3×#124—31no—
151C3×#124—31no—
152C3×#124—61no—
153C3×#123—61no—
154C3×#123—61no—
155C3×C22⋊Q8—61no—
156C3×C22⋊Q8—61no—
157C3×C22⋊Q8—61no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C3×C4×D4—61no—
166C2×C3×C4⋊C4—61no—
167#936—21no—
168#936C22×C311yescharacteristic
169#936C22×C311yescharacteristic
170#935—21no—
171#935—21no—
172D4×Dic3—21no—
173D4×Dic3C22×C311yescharacteristic
174D4×Dic3C22×C311yescharacteristic
175C2×#213C22×C311yescharacteristic
176C2×#213C22×C311yescharacteristic
177C2×#204C22×C311yescharacteristic
178#897—21no—
179#896—21no—
180#896—21no—
181#893C22×C311yescharacteristic
182#893C22×C311yescharacteristic
183D3×C4⋊C4—21no—
184#890C22×C311yescharacteristic
185#888C22×C311yescharacteristic
186C4×D12C22×C311yescharacteristic
187C4×Dic6C22×C311yescharacteristic
188C4×Dic6C22×C311yescharacteristic
189C3×#107—31no—
190C3×#107—31no—
191C3×#106—31no—
192C3×C4⋊C8—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#102—21no—
199C3×#102—21no—
200C3×#102—21no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102C2×D311yescharacteristic
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×#102C2×D311yescharacteristic
209C3×#102C22×C311yescharacteristic
210C3×#102C22×C311yescharacteristic
211C3×#102C22×C311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×#97—21no—
214C3×#97—31no—
215C3×#97C2×D311yescharacteristic
216C3×#97C22×C311yescharacteristic
217C3×C4×C8—31no—
218#832C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#821C22×C311yescharacteristic
221#818C22×C311yescharacteristic
222#816C22×C311yescharacteristic
223#815C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226C8×Dic3C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#808C22×C311yescharacteristic
230#807C22×C311yescharacteristic
231C4⋊(C3⋊C8)C22×C311yescharacteristic
232C23×C32—21no—
233C23×C32—21no—
234C22×C3×D3—21no—
235C32×D4—21no—
236C32×D4—21no—
237C32×D4—21no—
238C32×D4—21no—
239C32×D4—42no—
240C32×D4—81no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—81no—
250C2×C3×Dic3—81no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12#4112yes—
257C3×C4×D3—42no—
258C3×C4×D3—81no—
259C3×C4×D3—81no—
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3×Dic6—41no—
263C3×Dic6—81no—
264C32×C8—21no—
265C32×C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#559—31no—
269#554—31no—
270#490C3×D311yescharacteristic, complemented
271#489—31no—
272#488—31no—
273#479—31no—
274#478—31no—
275#474—31no—
276#463—31no—
277#463—31no—
278#459—31no—
279#446—31no—
280#442—31no—
281#440—31no—
282C4×D8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—31no—
293C2×C3×D4—41no—
294C2×C3×D4—41no—
295C2×C3×D4C22×D311yescharacteristic
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C23×C311yescharacteristic
298C2×C3×D4C23×C311yescharacteristic
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C2×D12C23×C311yescharacteristic
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×Dic6—21no—
311C2×Dic6C3×D411yescharacteristic
312C2×Dic6C23×C311yescharacteristic
313C3×SD16—62no—
314C3×D8—62no—
315C3×D8—62no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—31no—
319C2×C3×C8—31no—
320C2×C3×C8C22×D311yescharacteristic
321C2×C3×C8C22×D311yescharacteristic
322C2×C3×C8C23×C311yescharacteristic
323C2×C3×C8C23×C311yescharacteristic
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—41no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C4⋊C4C23×C311yescharacteristic
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—21no—
355C3×C42—31no—
356C3×C42—31no—
357C3×C42—61no—
358C3×C42C22×D311yescharacteristic
359C3×C42C23×C311yescharacteristic
360#217—21no—
361#217—21no—
362#217—21no—
363#217—21no—
364#217—21no—
365#217—21no—
366#213—22no—
367#213—22no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3C3×D411yescharacteristic
373C4⋊Dic3C23×C311yescharacteristic
374C4⋊Dic3C23×C311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4C3×D411yescharacteristic
379Dic3⋊C4C3×D411yescharacteristic
380C4×Dic3—21no—
381C4×Dic3C23×C311yescharacteristic
382C4×Dic3C23×C311yescharacteristic
383C2×C3⋊C8C23×C311yescharacteristic
384C2×C3⋊C8C23×C311yescharacteristic
385#204—22no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32C22×D411yescharacteristic
393C2×C3×D3—22no—
394C2×C3×D3—41no—
395C2×C3×D3—41no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—41no—
399C32×C4—41no—
400C32×C4C2×#4111yescharacteristic
401C32×C42−1+411yescharacteristic
402C3×Dic3—21no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C2×SD16—31no—
410C2×D8—31no—
411C2×D8—31no—
412C4⋊Q8—31no—
413#127C2×C3×D311yescharacteristic
414#125—31no—
415#125C2×C3×D311yescharacteristic
416#124—31no—
417#124—31no—
418#124—61no—
419#123—61no—
420#123—61no—
421C22⋊Q8—61no—
422C22⋊Q8—61no—
423C22⋊Q8—61no—
424C4×Q8—31no—
425C4×Q8—31no—
426C4×D4—31no—
427C4×D4—31no—
428C4×D4—31no—
429C4×D4—31no—
430C4×D4—31no—
431C4×D4—61no—
432C2×C4⋊C4—61no—
433#107—31no—
434#107—31no—
435#106—31no—
436C4⋊C8—31no—
437C4⋊C8—31no—
438C4⋊C8—31no—
439#103—31no—
440#103—31no—
441#103—31no—
442#102—31no—
443#102—31no—
444#102—31no—
445#102C2×C3×D311yescharacteristic
446#102C2×C3×D311yescharacteristic
447#102C2×C3×D311yescharacteristic
448#102C2×C3×D311yescharacteristic
449#97—31no—
450#97C2×C3×D311yescharacteristic
451C4×C8—31no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—61no—
459C22×D3—21no—
460C3×Q8—61no—
461C3×Q8—61no—
462C3×Q8—121no—
463C3×Q8—241no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—21no—
467C3×D4—21no—
468C3×D4—21no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—32no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—41no—
476C3×D4—41no—
477C3×D4—42no—
478C3×D4—42no—
479C3×D4—61no—
480C3×D4—82no—
481C3×D4—81no—
482C3×D4—81no—
483C3×D4—82no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—122no—
501C2×C3×C4—241no—
502C2×C3×C4—241no—
503C2×C3×C4—241no—
504C2×C3×C4—241no—
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4C2×C3×D411yescharacteristic
508C2×C3×C4C2×C3×D411yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C24×C311yescharacteristic
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—81no—
515C2×Dic3—81no—
516C2×Dic3C2×C3×D411yescharacteristic
517C2×Dic3C2×C3×D411yescharacteristic
518C2×Dic3C2×C3×D411yescharacteristic
519C2×Dic3C2×C3×D411yescharacteristic
520D12—21no—
521D12C3×#4112yes—
522C4×D3—42no—
523C4×D3—81no—
524C4×D3—81no—
525Dic6—21no—
526Dic6—21no—
527Dic6—41no—
528Dic6—81no—
529C3×C8—21no—
530C3×C8—21no—
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—41no—
534C3×C8—41no—
535C3×C8—61no—
536C3×C8—61no—
537C3⋊C8—21no—
538C3⋊C8—21no—
539C2×C32—81no—
540C2×C32—81no—
541C2×C32#54811yescharacteristic
542C2×C32#57511yescharacteristic
543C2×C32#57611yescharacteristic
544C3×D3—42no—
545C2×Q8—31no—
546C2×Q8—31no—
547C2×Q8—61no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—31no—
551C2×D4C22×C3×D311yescharacteristic
552C2×D4C22×C3×D311yescharacteristic
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558SD16—62no—
559D8—62no—
560D8—62no—
561C2×C8—31no—
562C2×C8—31no—
563C2×C8C22×C3×D311yescharacteristic
564C2×C8C22×C3×D311yescharacteristic
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—31no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4C22×C3×D311yescharacteristic
577C4⋊C4C22×C3×D311yescharacteristic
578C22⋊C4—61no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C22⋊C4—61no—
582C22⋊C4—61no—
583C22⋊C4—61no—
584C22⋊C4—61no—
585C22⋊C4—61no—
586C22⋊C4—61no—
587C42—31no—
588C42—31no—
589C42—61no—
590C42C22×C3×D311yescharacteristic
591C22×C3—21no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—62no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3C2×D3×D411yescharacteristic
614C22×C3C22×C3×D411yescharacteristic
615C2×D3—22no—
616C2×D3—41no—
617C2×D3—41no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—61no—
631C3×C4—61no—
632C3×C4—61no—
633C3×C4—61no—
634C3×C4—81no—
635C3×C4—81no—
636C3×C4—121no—
637C3×C4—121no—
638C3×C4—121no—
639C3×C4D3×#4111yescharacteristic
640C3×C4#101011yescharacteristic
641C3×C4C2×C3×#4111yescharacteristic
642C3×C4C3×2−1+411yescharacteristic
643Dic3—21no—
644Dic3—21no—
645Dic3—21no—
646Dic3—21no—
647Dic3—41no—
648Dic3—41no—
649Dic3—41no—
650C32#337011yescharacteristic, complemented, Sylow
651C23—21no—
652C23—21no—
653C23—61no—
654Q8—61no—
655Q8—61no—
656Q8—121no—
657Q8—241no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—32no—
663D4—42no—
664D4—61no—
665D4—81no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—122no—
676C2×C4—241no—
677C2×C4—241no—
678C2×C4—241no—
679C2×C4—241no—
680C2×C4C3×D3×D411yescharacteristic
681C2×C4C3×D3×D411yescharacteristic
682C2×C4C23×C3×D311yescharacteristic
683C8—21no—
684C8—21no—
685C8—61no—
686C8—61no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—81no—
691C2×C3—81no—
692C2×C3—81no—
693C2×C3—81no—
694C2×C3—122no—
695C2×C3—161no—
696C2×C3—161no—
697C2×C3#567711yescharacteristic
698C2×C3#577311yescharacteristic
699C2×C3#577411yescharacteristic
700C2×C3C3×#54811yescharacteristic
701C2×C3C3×#57511yescharacteristic
702C2×C3C3×#57611yescharacteristic
703D3—42no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—62no—
711C22—121no—
712C22—121no—
713C22C2×C3×D3×D411yescharacteristic
714C4—21no—
715C4—21no—
716C4—41no—
717C4—41no—
718C4—61no—
719C4—61no—
720C4—61no—
721C4—61no—
722C4—121no—
723C4—121no—
724C4—121no—
725C4C3×D3×#4111yescharacteristic
726C4C3×#101011yescharacteristic
727C3—21no—
728C3#8171011yescharacteristic, direct product factor
729C3C3×#337011yescharacteristic, complemented
730C2—81no—
731C2—81no—
732C2—122no—
733C2C3×#567711yescharacteristic
734C2C3×#577311yescharacteristic
735C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#490C2
socleC22×C32C22×D4
prime radicalC3×#5072C2
hypercenterC3×#490D3
hypocenterC3C3×#3370
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#490

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5713C2semidirect
2. C3×#5690C2semidirect
3. C32×#490C2semidirect
5. C3×#5063C2semidirect
6. C3×#4787C2semidirect
7. C3×#4787C2semidirect
8. C3×#4785C2semidirect
9. C3×#4768C2semidirect
10. C3×#4766C2semidirect
11. C3×#4765C2semidirect
12. C3×#4759C2semidirect
13. C3×#4756C2semidirect
14. C3×#4710C2semidirect
15. C3×#4701C2semidirect
17. #81710C3direct (N × H)
63. #5713C2×C3semidirect
64. #5690C2×C3semidirect
66. C3×#490D3semidirect
67. C3×#490C2×C3semidirect
81. #5063C2×C3semidirect
82. #4787C2×C3semidirect
83. #4787C2×C3semidirect
84. #4785C2×C3semidirect
85. #4768C2×C3semidirect
86. #4766C2×C3semidirect
87. #4765C2×C3semidirect
88. #4759C2×C3semidirect
89. #4756C2×C3semidirect
90. #4710C2×C3semidirect
91. #4701C2×C3semidirect
270. #490C3×D3semidirect
650. C32#3370semidirect
728. C3#81710direct (N × H)
729. C3C3×#3370semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#57132
C3×#56902
C32×#4902
C3×#50722
C3×#50632
C3×#47872
C3×#47852
C3×#47682
C3×#47662
C3×#47652
C3×#47592
C3×#47562
C3×#47102
C3×#47012
C3×#33703
#817103